Remark

Definition

Write

𝕀XHk:Π(X)→(Kk)Mod
\mathbb{I}_X^{H k} \;\colon\; \Pi(X) \to (K k)Mod

for the flat(∞,1)-module bundle which is constant on the chain complex concentrated on kk in degree 0, the tensor unit in [Π(X),(Hk)Mod]≃[Π(X),LqiCh•(kMod)][\Pi(X), (H k)Mod] \simeq [\Pi(X), L_{qi}Ch_\bullet(k Mod)].